Canopic clan: Difference between revisions

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~~[[Temperament]]s of the~~ '''mirkwai clan''' [[~~Tempering~~ out|~~temper~~ out]] the [[mirkwai comma]], {{monzo| 0 3 4 -5 }} = 16875/16807, a no-twos comma.

The '''mirkwai clan''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[mirkwai comma]] ({{monzo|legend=1| 0 3 4 -5 }}, [[ratio]]: 16875/16807), a no-twos comma.

== Canopus ==

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: mapping generators: ~3, ~7/5

~~: sval mapping generators: ~3, ~7/5~~

[[Optimal tuning]] ([[POTE]]): ~3 = 1901.9550{{c}}, ~7/5 = 583.9584{{c}}

[[Optimal tuning]] ([[POTE]]): ~3 = ~~1\1edt~~, ~7/5 = 583.9584

=== Overview to extensions ===

The full 7-limit extensions' relation to canopus is clearer if the mapping is normalized in terms of 3.5.7.2. In fact, the strong extensions are nusecond and octoid.

The full 7-limit extensions' relation to canopus is clearer if the mapping is normalized in terms of 3.5.7.2. In fact, the strong extensions are nusecond and octoid. These temperaments are distributed into different temperament collection pages.

* ''[[Nusecond]]'' (+126/125) → [[Starling temperaments #Nusecond|Starling temperaments]]

* ''[[Octoid]]'' (+4375/4374) → [[Ragismic microtemperaments #Octoid|Ragismic microtemperaments]]

The others are weak extensions. Mirkat tempers out [[19683/19600]], splitting the generator in two with a semitwelfth period. Sqrtphi tempers out [[15625/15552]], splitting the period in six. Miracle tempers out [[225/224]]. Pluto tempers out [[4000/3969]]. These split the generator in five. Quanharuk tempers out [[32805/32768]], splitting the generator in three with a 1/5-twelfth period. Semisept tempers out [[1728/1715]] and [[3136/3125]], splitting the generator in six. Kwai tempers out [[5120/5103]], splitting the generator in ten. Grendel tempers out [[6144/6125]], splitting the generator in eleven. Finally, eris tempers out [[65625/65536]], splitting the generator in sixteen.

Members of the clan ~~considered below are grendel, kwai, pluto, mirkat, eris, subsemifourth, septendesemi, gaster, subsedia, hemiseptisix, browser, and grazer. Discussed~~ elsewhere are:

Members of the clan discussed elsewhere are:

* ''[[Octokaidecal]]'' (+28/27 or 50/49) → [[Trienstonic clan #Octokaidecal|Trienstonic clan]]

* ''[[Meantritone]]'' (+81/80) → [[Meantone family #Meantritone|Meantone family]]

* ''[[Nusecond]]'' (+126/125) → [[Starling temperaments #Nusecond|Starling temperaments]]

* [[Miracle]] (+225/224) → [[Gamelismic clan #Miracle|Gamelismic clan]]

* ''[[Bohpier]]'' (+245/243) → [[Sensamagic clan #Bohpier|Sensamagic clan]]

* ''[[Semisept]]'' (+1728/1715 or 3136/3125) → [[Hemimean clan #Semisept|Hemimean clan]]

* ''[[Quinmage]]'' (+3125/3072) → [[Magic family #Quinmage|Magic family]]

* ''[[Octoid]]'' (+4375/4374) → [[Ragismic microtemperaments #Octoid|Ragismic microtemperaments]]

* [[Sqrtphi]] (+15625/15552) → [[Kleismic family #Sqrtphi|Kleismic family]]

* ''[[Quanharuk]]'' (+32805/32768) → [[Schismatic family #Quanharuk|Schismatic family]]

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* ''[[Quintiquart]]'' (+390625000/387420489) → [[Quartonic family #Quintiquart|Quartonic family]]

For ''no-twos'' extensions, see [[No-twos subgroup temperaments#Canopus]].

For ''no-twos'' extensions, see [[No-twos subgroup temperaments #Canopus]].

Considered below are grendel, kwai, pluto, mirkat, eris, subsemifourth, septendesemi, gaster, subsedia, hemiseptisix, browser, and grazer.

== Grendel ==

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 {{Technical data page}}
-[[Temperament]]s of the '''mirkwai clan''' [[Tempering out|temper out]] the [[mirkwai comma]], {{monzo| 0 3 4 -5 }} = 16875/16807, a no-twos comma.
+The '''mirkwai clan''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[mirkwai comma]] ({{monzo|legend=1| 0 3 4 -5 }}, [[ratio]]: 16875/16807), a no-twos comma.
 == Canopus ==
@@ Line 10: / Line 10: @@
 {{Mapping|legend=2| 1 3 3 | 0 -5 -4 }}
+: mapping generators: ~3, ~7/5
-: sval mapping generators: ~3, ~7/5
+[[Optimal tuning]] ([[POTE]]): ~3 = 1901.9550{{c}}, ~7/5 = 583.9584{{c}}
-[[Optimal tuning]] ([[POTE]]): ~3 = 1\1edt, ~7/5 = 583.9584
 [[Optimal ET sequence]]: [[13edt|b13]], [[62edt|b62]], [[75edt|b75]], [[88edt|b88]], [[101edt|b101]], [[114edt|b114]], [[355edt|b355]], [[469edt|b469]], [[583edt|b583]], [[697edt|b697]]
 === Overview to extensions ===
-The full 7-limit extensions' relation to canopus is clearer if the mapping is normalized in terms of 3.5.7.2. In fact, the strong extensions are nusecond and octoid.
+The full 7-limit extensions' relation to canopus is clearer if the mapping is normalized in terms of 3.5.7.2. In fact, the strong extensions are nusecond and octoid. These temperaments are distributed into different temperament collection pages.
+* ''[[Nusecond]]'' (+126/125) → [[Starling temperaments #Nusecond|Starling temperaments]]
+* ''[[Octoid]]'' (+4375/4374) → [[Ragismic microtemperaments #Octoid|Ragismic microtemperaments]]
 The others are weak extensions. Mirkat tempers out [[19683/19600]], splitting the generator in two with a semitwelfth period. Sqrtphi tempers out [[15625/15552]], splitting the period in six. Miracle tempers out [[225/224]]. Pluto tempers out [[4000/3969]]. These split the generator in five. Quanharuk tempers out [[32805/32768]], splitting the generator in three with a 1/5-twelfth period. Semisept tempers out [[1728/1715]] and [[3136/3125]], splitting the generator in six. Kwai tempers out [[5120/5103]], splitting the generator in ten. Grendel tempers out [[6144/6125]], splitting the generator in eleven. Finally, eris tempers out [[65625/65536]], splitting the generator in sixteen.
-Members of the clan considered below are grendel, kwai, pluto, mirkat, eris, subsemifourth, septendesemi, gaster, subsedia, hemiseptisix, browser, and grazer. Discussed elsewhere are:
+Members of the clan discussed elsewhere are:
 * ''[[Octokaidecal]]'' (+28/27 or 50/49) → [[Trienstonic clan #Octokaidecal|Trienstonic clan]]
 * ''[[Meantritone]]'' (+81/80) → [[Meantone family #Meantritone|Meantone family]]
-* ''[[Nusecond]]'' (+126/125) → [[Starling temperaments #Nusecond|Starling temperaments]]
 * [[Miracle]] (+225/224) → [[Gamelismic clan #Miracle|Gamelismic clan]]
 * ''[[Bohpier]]'' (+245/243) → [[Sensamagic clan #Bohpier|Sensamagic clan]]
 * ''[[Semisept]]'' (+1728/1715 or 3136/3125) → [[Hemimean clan #Semisept|Hemimean clan]]
 * ''[[Quinmage]]'' (+3125/3072) → [[Magic family #Quinmage|Magic family]]
-* ''[[Octoid]]'' (+4375/4374) → [[Ragismic microtemperaments #Octoid|Ragismic microtemperaments]]
 * [[Sqrtphi]] (+15625/15552) → [[Kleismic family #Sqrtphi|Kleismic family]]
 * ''[[Quanharuk]]'' (+32805/32768) → [[Schismatic family #Quanharuk|Schismatic family]]
@@ Line 37: / Line 36: @@
 * ''[[Quintiquart]]'' (+390625000/387420489) → [[Quartonic family #Quintiquart|Quartonic family]]
-For ''no-twos'' extensions, see [[No-twos subgroup temperaments#Canopus]].
+For ''no-twos'' extensions, see [[No-twos subgroup temperaments #Canopus]].
+Considered below are grendel, kwai, pluto, mirkat, eris, subsemifourth, septendesemi, gaster, subsedia, hemiseptisix, browser, and grazer.
 == Grendel ==